There is no way to substantiate that “Pyre Falcon Defence Combine is the Secure Commerce Commission registered conglomerate of subsidiary private military corporations acting in the interests of Kaalakiota. Wiyrkomi and Lai Dai Corporations” etc. etc. But what is the basis of rp then?
Actually, in this case, I think the statement you quoted can very much be substantiated.
The SCC is a part of CONCORD that manages the market we all trade on, in effect the claim is that DUTY. is indeed registered with CONCORD and interacts on the SCC managed market. An alliance of corporations can be a conglomerate of subsidiaries, all owned by a holding company. I am pretty sure DUTY.'s primary activities is shooting stuff thus PMC and I am pretty sure they are focused on shooting Feds in Black Rise and Placid thus are acting in the interests of KK, Wiyrkomi, and Lai Dai (who effectively own Black Rise and lay corporate claim to northern Placid).
So, the only area where any stretching need be done is regarding the SCC registration.
I find that a bit limited and boring these days though. Ingame mechanics are not always the best RP material, sadly. Sometimes they work, sometimes, they are just bland (i'm looking at you FW). But overall whatever you do ingame, it is mostly non consequential, or vain. What becomes interesting is not the fight between the Gallente Militia and the Caldari Militia over Mantenault per se, but what happens on the planet because of that... And what happened on the planet was pure world building, as usual.
I think part of the challenge with FW is the consequences and benefits of conquest are largely decoupled from the resources of the systems. Militia corporations are probably not knocking down POCOs in the systems they conqueror in order to setup their own and begin colonizing the planet with their own PI. So agreed, the mechanics can make things difficult.
However, taking the example of 4TH's planetary colonies - they actually exist in game and can be isolated. 4TH has a program by which any friendlies can request to temporarily join a 4TH corp, setup their colonies, and then leave and continue to access/maintain the colony. (I should probably write up some story around that).
If you want to claim planet-spanning holdings - train a few alts to do basic PI, form a small corporation, give your main all the shares, and say you have holdings on X number of planets and then list them if people say "no you don't!"